On Random-Oracle-Free Top-Level Secure Certificateless Signature Schemes

Certificateless public key cryptography (CL-PKC) overcomes the difficulties of the certificate managements in traditional public key infrastructure (PKI) and the key escrow problem in ID-Based public key cryptography (ID-PKC), concurrently. In 2018, Tseng et al. proposed a certificateless signature (CLS) scheme and claimed that their proposal is the first scheme which satisfies the security against the level-3 KGC (according to Girault's three categorizations of the honesty level of a trusted third party (TTP) which is proposed in 1991), in the standard model. However, we will show that unfortunately their scheme is even vulnerable against a malicious KGC. Afterwards, we will improve their scheme to be robust against the proposed attack. Finally, we will propose a CLS scheme secure against the level-3 KGC in the standard model, based on Yuan and Wang's CLS scheme. We will show that our proposal not only satisfies the level-3 security as well as the basic security requirements of a CLS scheme in the standard model, but also is more efficient than the previous works in the sense of computation and communication costs.